Vacuum formation behind the expansion wave in a piston motion problem

Abstract

Long time behavior of one-dimensional gas motion caused by pulling a piston with a high speed is numerically studied on the basis of the kinetic theory of gases. It is clarified that (i) if the piston speed is lower than a critical speed, the state of the gas time-asymptotically approaches the local equilibrium that corresponds to the isentropic solution in the conventional gas dynamics, namely, an expansion wave followed by a uniform state, and (ii) otherwise, there appears a highly nonequilibrium region with a very low pressure behind the expansion tail. In the latter case, the components of temperature parallel and perpendicular to the flow direction become highly different, and the density tends to vanish as time goes on, forming a vacuum region behind the tail at the infinite time.